Employing the concentration inequality as stated in [1]} with the parameters obtained in (REF ) and (REF ) we have that
\(\mathbf {P}\!\left(\mu \!\ge \!t\right) \!\le \!2\text{N}\exp \Bigg (\!\!&-\frac{t^2}{2} \Big [\frac{16 \text{N}^2}{9 Q^2} \rho _{\mathbf {\Psi }_k}^{(\text{L}_k)} \rho _{\mathbf {\Psi }_j}^{(\text{L}_j)} \max \left\lbrace \rho _{\mathbf {U}_k}^{(\text{S}_k)}, \rho _{\mathbf {U}_j}^{(\text{S}_j)}\right\rbrace  \\&+ \frac{t}{3} \frac{4\text{N}}{3\text{Q}} \kappa _{\mathbf {U}_{k}, \mathbf {U}_{j}}^{\left(\text{S}_k,\text{S}_j\right)} \kappa _{\mathbf {\Psi }_{k}, \mathbf {\Psi }_{j}}^{\left(\text{L}_k,\text{L}_j\right)} \Big ]^{-1}\Bigg ).\) 
